Spectral analysis of wave propagation through rows of scatterers via random sampling and a coherent potential approximation

Abstract

A method is proposed for determining the modal spectra of waves supported by arrays, which are composed of multiple rows of scatterers randomly disordered around an underlying periodic configuration. The method is applied to the canonical problem of arrays of identical small acoustically soft circular cylinders and disorder in the location of the rows. Two different approaches are adopted to calculate the modes: (i) forming an ensemble average of the modes from individual realizations (loosely: extract information, then average); and (ii) extracting the modes from the ensemble average wave field (loosely: average, then extract information). Differences in the attenuation rates predicted by the two approaches, which cannot be attributed to numerical errors, are found for problems involving multiple wave directions and large disorder. A form of the coherent potential approximation (CPA) is also devised. Comparisons of the CPA to the results given by random sampling show that it gives high accuracy. © 2013 Society for Industrial and Applied Mathematics.